Tuesday, February 19, 2013

Weight: Place it Carefully

Over the past few years I have written several articles, speed tips, and answers to questions that relate to weight position. Today, I’d like to bring this information together into one article. I realize that some of this information is a repeat, but I hope that each of you will find a few nuggets of information that you can put to good use.

TERMS

First, let’s get some terms defined:

COG: Center of gravity - the location at which an object balances in all three dimensions. In this article it will strictly refer to the lengthwise and height-wise point at which the car balances (also known as the horizontal COG and vertical COG).

Weight Position: the location on the car where the added ballast weight is placed. Note that weight position affects, but is not the same as the COG,

Wheelbase: the distance between the front and back axles.

LOCATING THE COG

The horizontal COG of a pinewood derby car can be easily located as follows: (1) set a balance stand (or a ruler on its long edge) on a table and (2) lay the car (with wheels and axles in place) on the device as shown in Figure 1. Move the car forward or backward until it balances on the ruler. This point at which the car balances is the horizontal COG.


Figure 1 - Locating the COG

HORIZONTAL COG - FRONT TO BACK

Due to track differences there is no one best horizontal COG. In fact, the horizontal COG that produces best results on one track will likely not produce the best results on another track.

There are three track types in use today (see Figure 2), with type 2 being the most predominant:

1. Continuous-slope - One continuous slope from the starting line to the finish line.

2. Ramp-flat - Starts on a slope, then transitions to a long flat section.

3. S-shaped - Starts on a slope, transitions to a steeper slope, and then transitions to a flat section).


Figure 2 - Track Types

For the continuous-slope track, the horizontal COG of the car has only a minor effect on car performance (due to uneven weight distribution on the wheels), but it is best to locate the COG near the middle of the car body.

For the ramp-flat track, best performance is obtained offsetting the horizontal COG towards the rear of the car. The actual location varies from track to track, but a good rule of thumb is 1 inch in front of the rear axle. This location should be adjusted based on the following track features:

- Length: longer tracks (over 50 feet) require a COG closer to the center of the car. Due to the offset COG, the rear wheels will bear more weight than the front wheels. On tracks with a long flat section, this extra rear friction will result in a faster speed loss.

- Smoothness: To maintain stability, rougher tracks may require a COG closer to the center of the car.

Why is the horizontal COG offset to the rear on this type of track. With an offset horizontal COG, the car will have a longer fall distance and will thus achieve a faster speed at the bottom of the hill (see Figure 3).


Figure 3 - Fall Distance Based on COG Position

For the S-shaped track, the best location of the COG depends on the length of each section. But, in the absence of track testing (see below) it is best to locate the COG similar to the ramp-flat track.

TESTING THE TRACK FOR HORIZONTAL COG

Testing for the best horizontal COG location for a given track is fairly easy if you have a track timer. Build a lightweight car without added weight, but with three dowel rod pieces sticking up out of the car (one in front, one in back, and one in the middle). Using steel washers weight the car in the front, back, and middle and compare the results. Mix and match to find the best COG for the track.

I ran time trials with this type of test car on a 32 foot ramp-flat track and found that rear-weighted cars outperformed front-weighted cars by up to one car length. Other testing results posted on the internet show similar results.

VERTICAL COG - UP AND DOWN

Let’s now move on to the vertical position of the weight. Is it better to have a high center of gravity (HCG) or a low center of gravity (LCG)? A LCG car will tend to be more stable, but it would seem that a HCG would impart more speed to the car. But is this really true?

In fact, it isn't. Given two cars with the center of gravity at the same lengthwise location, but with one having the center of gravity low on the car, while the other has the center of gravity high on the car, the LCG car will fall a greater distance. Referring to Figure 4, note that because of the starting ramp angle, the fall distance for the HCG car is actually less than the fall distance of the LCG car. The actual difference is based on the slope angle. But on this hypothetical
track, the HCG car falls only 96.6% of LCG car's fall distance.


Figure 4 - Effect of Vertical Weight Position on Fall Distance

Although the LCG car will attain a higher speed, due to a pendulum effect the HCG car will traverse the curved portion of the track slightly faster than the low center of gravity car. But unless the flat section of the track is very short, the LCG car will overtake the HCG car on the flat section.

OTHER CONSIDERATIONS

Here are several other factors to consider when locating the weight

Type of weight - The actual weight type does not affect the speed of the car, but does affect how easily the COG can be placed as desired. Denser weight (such as tungsten) allows much greater flexibility in weight placement than does less dense weight (such as zinc).

Length of car - Longer cars allow the horizontal COG to be moved further to the rear (it also allows a longer wheelbase which aids in stability and alignment). So it is generally best to maintain the longest possible car body.

Raised Wheel - A raised front wheel necessitates a rearward adjusted horizontal COG.

Wheel Weight - The horizontal COG must be measured with the wheels and axles installed. So, lighter wheels (such as our Outlaw Wheels) allow more flexibility in horizontal COG placement.

Wheelbase - The location of the axles affects the location of the COG. Specifically, the position of the rear axle sets a limit on rearward placement of the horizontal COG. As noted in Figure 5, simply using the axle slot closest to the end of the block as the rear axle allows a 5/8 inch rearward movement of the horizontal COG.


Figure 5 - Effect of Block Orientation on the Horizontal COG

CONCLUSION

The COG has a significant effect on the performance of the car. If possible, find out the specifics of the target track and design your car for optimal performance.

From Pinewood Derby Times Volume 5, Issue 10

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